Abstract

Let $\pi$ be an $\mathrm{SL}(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove that there is a computable absolute constant $\delta>0$ such that $$ L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll_{\pi} M^{\frac{3}{4}-\delta}. $$